2019/04/16 by Sebastian Baader, Baader, Sebastian, Luca Studer +3
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG
paper · pdf · doi:10.48550/arxiv.1904.07824
9 pages, 1 figure
arxiv created 2019/04/16 · arxiv updated 2019/04/17
It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in \mathbb R3. In this note we show that distortion minimisers exist among convex embedded 2-spheres and have uniformly bounded eccentricity. Moreover, we prove that π/2 is a sharp lower bound on the distortion of embedded closed surfaces of positive genus.